The 35-year-old was reported missing four-and-a-half years ago after she failed to turn up for work at York University.
Despite a high-profile investigation by North Yorkshire Police, involving up to 100 officers, no trace of Miss Lawrence has been found.
Detectives have stressed that the new review of the case has not been prompted by any important fresh lead.
Miss Lawrence's family has mounted a high-profile campaign to keep the case in the headlines and her father, Peter Lawrence, welcomed the move. He said: "Without being too hopeful, it does give you some hope. There have been advances. They are able to look at this afresh and any opportunity at all to find out for the family and for friends what happened to Claudia is obviously to be welcomed."
Miss Lawrence's terrace house in the Heworth area of York has not been lived in since she failed to turn up for work in March 2009. Her father said police had exclusive possession of the house for 18 months and it had been left since then.
Asked how the house is, he said: "It's feeling sad, if I can describe a house like that. It's not been lived in for four-and-a-half years."
Police said one reason they were searching the house was due to the possibility it could be occupied again in the future.